Abstract
In this paper, we discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach. Topological properties such as compactness, closedness, and net theory are used in the proof. The admissibility of the function space topology and KKM-Theorem have played important role in proving the results.
Highlights
Variational inequalities have appeared as a working and important tool to investigate various fields of mathematics as well as of sciences including elasticity, vector equilibrium problems, and optimization problems [1,2,3,4]
Here, we investigate a generalized nonlinear variational like inequality problem, which was proposed by Farajzadeh et al [9] as follows: Generalized nonlinear variational-like inequality problem: let hX, X∗i be a dual system of Hausdorff topological vector spaces and K be a nonempty convex subset of X
We consider two variants of nonlinear vector variational-like inequality problems in a more general setup as follows: Let X and Y be two topological vector spaces, and let K be a nonempty, closed, and convex subset of X and CLðX, YÞ be the space of all continuous linear mappings from the space X to the space Y
Summary
Ankit Gupta ,1 Satish Kumar, Ratna Dev Sarma, Pankaj Kumar Garg, and Reny George 4. Received 30 April 2021; Revised 1 July 2021; Accepted 7 July 2021; Published 28 July 2021. We discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach. Topological properties such as compactness, closedness, and net theory are used in the proof. The admissibility of the function space topology and KKM-Theorem have played important role in proving the results
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